Framework gives conjectural characterization of geometric families of abelian varieties with unbounded average l-Selmer sizes, proven correct when l-torsion module is constant across the family.
arXiv preprint arXiv:2103.08530 , year=
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Establishes group presentations for quotients of G_∅^T(K) in Γ-extensions and derives a random model predicting the distribution of these Galois groups over arbitrary global base fields Q.
Survey of advances proving Cohen-Lenstra heuristics for 2-primary and ell-primary parts of class groups, including resolutions of the minimalist conjecture for elliptic curves and Stevenhagen's conjecture on the negative Pell equation.
citing papers explorer
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Tamagawa ratios and unbounded Selmer moments
Framework gives conjectural characterization of geometric families of abelian varieties with unbounded average l-Selmer sizes, proven correct when l-torsion module is constant across the family.
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Presentations of Galois groups of unramified extensions of global fields and its predicted distribution
Establishes group presentations for quotients of G_∅^T(K) in Γ-extensions and derives a random model predicting the distribution of these Galois groups over arbitrary global base fields Q.
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Recent Progress around Cohen-Lenstra Heuristics
Survey of advances proving Cohen-Lenstra heuristics for 2-primary and ell-primary parts of class groups, including resolutions of the minimalist conjecture for elliptic curves and Stevenhagen's conjecture on the negative Pell equation.